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KNIGHTS is a superb chess based puzzle game. I enjoyed LYNE too, especially it's beautiful music. My absolute favourite puzzle game is Talos Principle, though.

I'm looking forward to playing other puzzle games like Human Fall Flat and Niko: Through the Dream in the future. As for puzzles with more minimalist design, I currently have the first Quell game in my library but I haven't had a chance to play it yet. Did you play it?

http://www.mobygames.com/game/dos/are-we-there-yet if you are non american this might actually be difficult and challenging at some puzzles. And a few games by this guy http://www.mobygames.com/developer/sheet/view/developerId,13401/
I would like to see more puzzle games like that.

And curious about this game. http://store.steampowered.com/app/210970/

LYNE, Snakebird, SpaceChem and Sokobond..

All nice puzzle games..

Defense Grid: The Awakening. It becomes a puzzle game when you're trying to optimize your solutions to max your scores for leaderboards.

The Room is one of those great puzzle games I'd like to recommend. LYNE is pretty good too and make sure to check Monument Valley for IOS and android :)

There are also some titles that I haven't tried like Zenge for instance.

Missed it. Arr. Didn't help that the last message was 3 days ago. Oh well. Snakebird is probably my favorite puzzle game that I've played in a while. Well, The Witness is too but you gotta... draw the line...
I think I'd enjoy Sokobond, but I should just pick it up during a sale next time.